Finite Group Databasebeta

← #44505963

Subgroups — #44505963

Order 30848.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D241C211yesmaximal, characteristic
2#29507679C211yesmaximal, characteristic
3#29507564C211yesmaximal, characteristic
4#29507455C211yesmaximal, characteristic, complemented
5#29507454C211yesmaximal, characteristic, complemented
6#29507453C211yesmaximal, characteristic, complemented
7#328×C241C211yesmaximal, characteristic, complemented
8C2×Q8×D241C411yescharacteristic, complemented
9C22×C4×D241C2211yescharacteristic
10C2×#16838753—21no—
11#21440622C411yescharacteristic, complemented
12#21440621C2211yescharacteristic
13#21440620—21no—
14#21440619—21no—
15#21440618C411yescharacteristic, complemented
16C4⋊C4×D241—21no—
17C4⋊C4×D241C411yescharacteristic, complemented
18C2×#16838747—21no—
19C22⋊C4×D241—21no—
20C2×C4×Dic241—21no—
21C22⋊#14515349C2211yescharacteristic
22#21440554—21no—
23#21440549C2211yescharacteristic
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C23×D241D411yescharacteristic
28C2×Dic482—21no—
29C2×Dic482C2×C411yescharacteristic
30Q8×D241—42no—
31C22×Dic241—21no—
32C22×Dic241D411yescharacteristic
33C2×C4×D241—21no—
34C2×C4×D241—21no—
35C2×C4×D241—42no—
36C2×C4×D241C2×C411yescharacteristic
37C2×C4×D241C2×C411yescharacteristic
38C2×C4×D241D411yescharacteristic
39C2×C4×D241D411yescharacteristic
40#16838753—42no—
41C2×#14515349—21no—
42C4⋊Dic241—21no—
43C4⋊Dic241C2×C411yescharacteristic
44#16838749—21no—
45#16838749—21no—
46#16838749—21no—
47C22⋊Dic241—21no—
48#16838747—24no—
49#16838747—21no—
50#16838747—21no—
51C4×Dic241—42no—
52C2×Q8×C241C2×C411yescharacteristic
53C22×C4×C241—21no—
54C22×C4×C241C2311yescharacteristic
55C2×C8×C241—21no—
56C4⋊C4×C241—21no—
57C4⋊C4×C241C2×C411yescharacteristic
58C22⋊C4×C241—21no—
59C22×D241—21no—
60C22×D241—21no—
61C22×D241—22no—
62C22×D241—41no—
63C22×D241C22⋊C411yescharacteristic
64C22×D241C22⋊C411yescharacteristic
65Dic482—42no—
66Dic482—41no—
67C2×Dic241—22no—
68C2×Dic241—22no—
69C2×Dic241—21no—
70C2×Dic241—21no—
71C2×Dic241—41no—
72C2×Dic241—41no—
73C2×Dic241C22⋊C411yescharacteristic
74C2×Dic241C22⋊C411yescharacteristic
75C4×D241—22no—
76C4×D241—22no—
77C4×D241—41no—
78C4×D241—41no—
79C4×D241—42no—
80C4×D241—42no—
81#14515349—41no—
82C23×C241C2×D411yescharacteristic
83Q8×C241—41no—
84C2×C4×C241—22no—
85C2×C4×C241—21no—
86C2×C4×C241—21no—
87C2×C4×C241—41no—
88C2×C4×C241—41no—
89C2×C4×C241—41no—
90C2×C4×C241C22×C411yescharacteristic
91C2×C4×C241C2×D411yescharacteristic
92C8×C241—41no—
93C22×C241—21no—
94C22×C241—21no—
95C22×C241C2×C22⋊C411yescharacteristic
96C22×C241#13711yescharacteristic
97C22×C241#13711yescharacteristic
98C2×D241—21no—
99C2×D241—21no—
100C2×D241—21no—
101C2×D241—21no—
102C2×D241—21no—
103C2×D241—42no—
104C2×D241—42no—
105C2×D241#10412yes—
106C4×C241—21no—
107C4×C241—21no—
108C4×C241—42no—
109C4×C241—41no—
110C4×C241—41no—
111Dic241—21no—
112Dic241—42no—
113Dic241—41no—
114Dic241—41no—
115Dic241#9912yes—
116C2×C241—21no—
117C2×C241—21no—
118C2×C241C2×#9911yescharacteristic
119C2×C241#41911yescharacteristic
120C2×C241C2×#10411yescharacteristic
121D241—22no—
122D241—41no—
123C241#150811yescharacteristic, complemented, Sylow
124#1508—2411nomaximal, Sylow
125C2×C22⋊Q8—2411no—
126#407—2411no—
127C4×C22⋊C4—2411no—
128#328—2411no—
129#328—2411no—
130#328—2411no—
131#328D24111yescharacteristic, complemented
132C22×Q8—2411no—
133C23×C4—2411no—
134C2×M16—4821no—
135C22⋊Q8—4821no—
136C22⋊Q8—4821no—
137C22⋊Q8—2411no—
138C22⋊Q8—2411no—
139C22⋊Q8—2411no—
140C22⋊Q8C2×D24111yescharacteristic
141C2×C4⋊C4—4821no—
142C2×C4⋊C4—2411no—
143C2×C22⋊C4—4821no—
144C2×C22⋊C4—4821no—
145C2×C42—4821no—
146C22⋊C8—4821no—
147C22⋊C8—2411no—
148C22⋊C8C2×D24111yescharacteristic
149#95—2411no—
150#95C2×D24111yescharacteristic
151C24—2411no—
152C2×Q8—9642no—
153C2×Q8—4821no—
154C2×Q8—2411no—
155C2×Q8C4×D24111yescharacteristic
156C22×C4—21no—
157C22×C4—9642no—
158C22×C4—4821no—
159C22×C4—4821no—
160C22×C4—4821no—
161C22×C4—2411no—
162C22×C4—2411no—
163C22×C4—2411no—
164C22×C4—2411no—
165C22×C4—2411no—
166C22×C4C22×D24111yescharacteristic
167M16—9642no—
168C2×C8—21no—
169C2×C8—4821no—
170C4⋊C4—21no—
171C4⋊C4—4821no—
172C4⋊C4—4821no—
173C4⋊C4—4821no—
174C4⋊C4—4821no—
175C4⋊C4—2411no—
176C4⋊C4C4×D24111yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—4824no—
179C22⋊C4—4821no—
180C22⋊C4—4821no—
181C22⋊C4—4821no—
182C42—9642no—
183C23—9641no—
184C23—4822no—
185C23—4821no—
186C23—4821no—
187C23—2411no—
188C23—2411no—
189C23D4×D24111yescharacteristic
190Q8—41no—
191Q8—9641no—
192Q8—9642no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—9641no—
200C2×C4—9641no—
201C2×C4—9642no—
202C2×C4—9642no—
203C2×C4—9641no—
204C2×C4—9641no—
205C2×C4—4822no—
206C2×C4—4822no—
207C2×C4—4822no—
208C2×C4—4821no—
209C2×C4—4821no—
210C2×C4—4822no—
211C2×C4—2411no—
212C2×C4—2411no—
213C2×C4C2×C4×D24111yescharacteristic
214C2×C4D4×D24111yescharacteristic
215C8—41no—
216C8—9641no—
217C22—21no—
218C22—21no—
219C22—9642no—
220C22—9642no—
221C22—4821no—
222C22—4821no—
223C22—4821no—
224C22—4821no—
225C22—4821no—
226C22—2412no—
227C22C22⋊C4×D24111yescharacteristic
228C22#2144067111yescharacteristic
229C22#2144067411yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—41no—
235C4—9642no—
236C4—9641no—
237C4—9641no—
238C4—4821no—
239C4—2412no—
240C2—21no—
241C2—21no—
242C2—9641no—
243C2—4822no—
244C2#99×D24111yescharacteristic
245C2#2950772411yescharacteristic
246C2#104×D24111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC23×D241D4
cosocleC22×C4×C241C23
hypercenter#328D241
hypocenterC241#1508
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #29507455C2semidirect
5. #29507454C2semidirect
6. #29507453C2semidirect
7. #328×C241C2semidirect
8. C2×Q8×D241C4semidirect
11. #21440622C4semidirect
15. #21440618C4semidirect
17. C4⋊C4×D241C4semidirect
123. C241#1508semidirect
131. #328D241semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22⋊Q8×D2412
#295076792
#295075642
#295074552
#295074542
#295074532
#328×C2412
#1508241